A middle school decided to run the following spinner game as a fund-raiser on Christmas Carnival.
Making Purple : Spin each spinner once. Blue and red make purple. So, if one spinner shows Red (R) and the other shows Blue (B), you win. Such an outcome is denoted as a win.
Generated by claude-sonnet-4-6 · 2026-06-15 10:30 · grounding stimulus
Model Answer
(i) All possible outcomes:
Assuming Spinner 1 has Red (R) and Blue (B), and Spinner 2 has Red (R) and Blue (B):
Possible outcomes = {(R, R), (R, B), (B, R), (B, B)}
(ii) Probability of making purple:
Winning outcomes (one R and one B) = (R, B) and (B, R) → 2 outcomes
$$P(\text{purple}) = \frac{2}{4} = \frac{1}{2}$$
(iii)
Out of 99 participants:
- Winners = $99 × \frac{1}{2} ≈ 50$ (approximately), Losers = 49
- School collects from losers: $49 × ₹5 = ₹245$
- School pays winners: $50 × ₹10 = ₹500$
- Net fund collected = ₹245 − ₹500 = −₹255 (school loses ₹255)
OR
If ₹5 for both win and loss:
- Winners = 50, Losers = 49
- School collects from losers: $49 × ₹5 = ₹245$
- School pays winners: $50 × ₹5 = ₹250$
- Net fund = ₹245 − ₹250 = −₹5 (school loses ₹5)
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Explanation
- Part (i): Examiners expect all 4 sample space outcomes listed clearly.
- Part (ii): Two outcomes constitute a win, so probability = 2/4 = 1/2. This is the key fraction to use in part (iii).
- Part (iii): With 99 participants and P(win) = 1/2, split as ~50 winners and 49 losers. Calculate inflow (from losers) minus outflow (to winners). In the main case the school actually loses money — write that clearly. The OR part similarly yields a small net loss. Show all steps for full marks.